What is the diameter of a bicycle wheel if it is known that the wheel, rolled in 1727, turns 1000 times.
consider the approximate value of pi to be 3.14.
We can use the formula:
circumference of wheel = diameter x pi
Let's first find the circumference of the wheel, which we know is equal to the distance it travels when it rolls 1000 times. We don't know the actual distance, but we can use the number of rotations and assume that each rotation covers the circumference of the wheel:
circumference of wheel x 1000 = distance traveled
Now we can rearrange the formula to solve for the diameter:
diameter = distance traveled / (pi x 1000)
Using the values given, we have:
circumference of wheel x 1000 = distance traveled
circumference of wheel = distance traveled / 1000
circumference of wheel = 1727 / 1000 (assuming the units are in meters or some other standard unit)
circumference of wheel = 1.727 meters
diameter = 1.727 / (3.14 x 1000)
diameter = 0.00055 meters or 0.55 millimeters (rounded to the nearest hundredth)
Therefore, the diameter of the bicycle wheel is approximately 0.55 millimeters.
A paper bag contains three1 dollar bills to five dollar bill six $10 bills and one $20 bill in army select and keep one bill for the bag find Lenaerts expect to gain
To find Lenaert's expected gain, we need to calculate the average value of a single bill if he selects and keeps one bill from the bag.
First, let's calculate the total value of all the bills in the bag:
3 x $1 = $3
5 x $5 = $25
6 x $10 = $60
1 x $20 = $20
Total value = $3 + $25 + $60 + $20 = $108
Now, let's calculate the probability of selecting each type of bill:
Probability of selecting a $1 bill = 3/15 = 0.2
Probability of selecting a $5 bill = 5/15 = 0.33
Probability of selecting a $10 bill = 6/15 = 0.4
Probability of selecting a $20 bill = 1/15 = 0.067
Finally, we can calculate the expected value of a single bill with the formula:
Expected value = (probability of selecting a bill) x (value of the bill)
So Lenaert's expected gain if he selects and keeps one bill from the bag is:
(0.2 x $1) + (0.33 x $5) + (0.4 x $10) + (0.067 x $20) = $1.69
Therefore, Lenaert can expect to gain an average of $1.69 if he selects and keeps one bill from the bag.
To find the diameter of a bicycle wheel, we can use the formula for circumference, which relates the circumference to the diameter:
C = πd
where C is the circumference and d is the diameter.
In this case, we are given that the wheel, when rolled, turns 1000 times. The distance traveled by the wheel in one complete revolution (or one turn) is equal to the circumference of the wheel.
Since we don't have the exact circumference value, we'll use an approximation of π as 3.14.
Step 1: Calculate the distance traveled in 1000 revolutions
The distance traveled in 1000 revolutions can be found by multiplying the circumference by 1000:
Distance_traveled = C * 1000
Step 2: Solve for the circumference
Rearranging the formula, we have:
C = Distance_traveled / 1000
Step 3: Calculate the diameter
Using the circumference formula, we can substitute the calculated value for the circumference into the formula:
C = πd
Simplifying, we get:
d = C / π
Step 4: Substitute values and solve for diameter
Substituting the calculated value for the circumference into the formula, we have:
d = Distance_traveled / (1000 * π)
Now, you can plug in the values and calculate the diameter:
d = Distance_traveled / (1000 * 3.14)
Please note that without the actual distance traveled in one turn, we cannot provide an accurate answer, but you can use this methodology to calculate the diameter based on the given information.